Heights of Ceresa and Gross-Schoen cycles
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908791736369152 |
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| author | Gao, Ziyang Zhang, Shou-Wu |
| author_facet | Gao, Ziyang Zhang, Shou-Wu |
| contents | We study the Beilinson-Bloch heights of Ceresa and Gross-Schoen cycles in families. We construct that for any $g\ge 3$, a Zariski open dense subset $\mathcal{M}_g^{\mathrm{amp}}$ of $\mathcal{M}_g$, the coarse moduli of curves of genus $g$ over $\mathbb{Q}$, such that the heights of Ceresa cycles and Gross-Schoen cycles over $\mathcal{M}_g^{\mathrm{amp}}$ have a lower bound and satisfy the Northcott property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Heights of Ceresa and Gross-Schoen cycles Gao, Ziyang Zhang, Shou-Wu Number Theory Algebraic Geometry 11G35, 11G50, 14C25 We study the Beilinson-Bloch heights of Ceresa and Gross-Schoen cycles in families. We construct that for any $g\ge 3$, a Zariski open dense subset $\mathcal{M}_g^{\mathrm{amp}}$ of $\mathcal{M}_g$, the coarse moduli of curves of genus $g$ over $\mathbb{Q}$, such that the heights of Ceresa cycles and Gross-Schoen cycles over $\mathcal{M}_g^{\mathrm{amp}}$ have a lower bound and satisfy the Northcott property. |
| title | Heights of Ceresa and Gross-Schoen cycles |
| topic | Number Theory Algebraic Geometry 11G35, 11G50, 14C25 |
| url | https://arxiv.org/abs/2407.01304 |